Which of these polynomial equations is of least degree and has -1, 2, and 4 as three of its roots? 5x2 + 2x + 8 = 0 (x + 2)(x - 1)(x + 4) = 0 x3 - 5x2 + 2x + 8 = 0 x4 - x3 - 5x2 + 2x + 8 = 0

This would be a great place to apply synthetic division.

Is -1 a root of 5x^2 + 2x + 8 = 0? To find out, use -1 as divisor in synth. div."

-1 / 5 2 8

-5 3

5 -3 11 Since there's a remainder of 11, -1 is NOT a root of

5x^2 + 2x + 8 = 0. Move on to the next quadratic:

(x + 2)(x - 1)(x + 4). x=-1 is not a root. Move on to the next polynomial:

x^3 - 5x^2 + 2x + 8 = 0

Is -1 a root of that? Set up and carry out the synth. div.:

-1 / 1 -5 2 8

-1 6 -8

1 -6 8 0 This zero remainder tells us that -1 IS a root of

x^3 - 5x^2 + 2x + 8 = 0.

Move on to the next polynomial: x^4 - x^3 - 5x^2 + 2x + 8 = 0

Determine, using synth. div., whether -1 is or is not a root.

Once you've eliminated one or more of the polynomials,

You must, of course, determine whether or not 2 and 4 are roots.

The answer to this problem is the polynomial whose roots include -1, 2 and 4. This does not necessarily rule out the final choice, which has four roots.